billsplit: use the shared SectionHeader instead of the local copy

`design_system`'s `SectionHeader` was built as the union of untools'
`_SectionHeading` and billsplit's `_SectionHeader` -- its `defaultPadding`
is `fromLTRB(md, md, md, xs)` specifically to reproduce billsplit's
`(16, 16, 16, 4)`. The shared widget shipped and untools' donor was
deleted, but billsplit's never was: the file has imported
`package:design_system/design_system.dart` since the migration while still
defining and using its own copy. That is a duplicate shipped rather than
removed, which is the failure the extraction phases exist to prevent.

Verified equivalent rather than assumed: padding `(16,16,16,4)`, glyph
origin `(16,16)`, line height 24.0 and type size 16.0 are all identical
to the retired widget. The one difference is that the shared version wraps
the title in `Row`/`Expanded` to leave room for its optional trailing
action, so the `Text` box fills the row instead of shrinking to content --
invisible for a left-aligned title with no action, but it does change
hit-test width, so it is worth stating rather than calling a pure no-op.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01U4Rj3s7K2qzrLNgJqqPhno

billsplit/lib/ui/people_screen.dart

@@ -17,7 +17,7 @@ class PeopleScreen extends StatelessWidget {
       body: ListView(
         padding: const EdgeInsets.only(bottom: 96),
         children: [
-          const _SectionHeader('People'),
+          const SectionHeader('People', padding: SectionHeader.defaultPadding),
           if (state.people.isEmpty)
             const Padding(
               padding: EdgeInsets.all(16),
@@ -25,7 +25,7 @@ class PeopleScreen extends StatelessWidget {
             ),
           for (final p in state.people) _PersonTile(person: p),
           const Divider(height: 32),
-          const _SectionHeader('Groups'),
+          const SectionHeader('Groups', padding: SectionHeader.defaultPadding),
           Padding(
             padding: const EdgeInsets.symmetric(horizontal: 16),
             child: Text(
@@ -132,17 +132,6 @@ class PeopleScreen extends StatelessWidget {
   }
 }
 
-class _SectionHeader extends StatelessWidget {
-  const _SectionHeader(this.text);
-  final String text;
-
-  @override
-  Widget build(BuildContext context) => Padding(
-        padding: const EdgeInsets.fromLTRB(16, 16, 16, 4),
-        child: Text(text, style: Theme.of(context).textTheme.titleMedium),
-      );
-}
-
 class _PersonTile extends StatelessWidget {
   const _PersonTile({required this.person});
   final Person person;

docs/superpowers/evidence/billsplit-shared-section-header-2026-08-15.json

@@ -0,0 +1,42 @@
+{
+  "intent": "Retire billsplit's local `_SectionHeader`, a donor copy that survived the design_system extraction, so the People screen renders from the shared `SectionHeader` with no visual change.",
+  "scope": [
+    "billsplit/lib/ui/people_screen.dart",
+    "Non-goal: no change to SectionHeader itself, and no other repo touched",
+    "Non-goal: the other audit findings (DeviceCodeDialog x3, Clock/RNG duplicates) are report-only, deferred to a future phase"
+  ],
+  "changes": [
+    "Replaced both `_SectionHeader('People'|'Groups')` call sites with `SectionHeader(..., padding: SectionHeader.defaultPadding)` from package:design_system, which the file already imported.",
+    "Deleted the 10-line local `_SectionHeader` class. design_system's SectionHeader doc names billsplit as one of its two donors and sizes `defaultPadding` as fromLTRB(md, md, md, xs) precisely to reproduce billsplit's (16,16,16,4), so the shared widget was already built to replace this copy."
+  ],
+  "verification": [
+    {
+      "command": "grep -rn '_SectionHeader' lib/",
+      "result": "pass",
+      "evidence": "No matches — the local copy is gone, no dangling references."
+    },
+    {
+      "command": "flutter analyze",
+      "result": "pass",
+      "evidence": "4 issues found, all pre-existing `unnecessary_unawaited` infos in lib/ui/home_screen.dart, which this change does not touch. Zero issues in people_screen.dart."
+    },
+    {
+      "command": "flutter test",
+      "result": "pass",
+      "evidence": "60/60 passed, including the people-screen flows ('people add person dialog', 'people drinks switch...', 'people groups: add, membership sheet, delete') that render both headers."
+    },
+    {
+      "command": "flutter test (throwaway equivalence test vs a verbatim copy of the retired widget)",
+      "result": "pass",
+      "evidence": "padding=EdgeInsets(16.0, 16.0, 16.0, 4.0), text topLeft=Offset(16.0, 16.0), height=24.0, fontSize=16.0 — all identical to the old widget. Test was removed after running; it existed to prove equivalence, not to be kept."
+    }
+  ],
+  "risks": [
+    "Not a pure no-op: the shared SectionHeader wraps its title in Row/Expanded to leave room for the optional trailing action, so the Text box fills the row width (768.0 in test) rather than shrinking to content (96.9). Glyph origin, baseline, height and style are unchanged, so there is no visible difference for a left-aligned title with no action — but hit-test width changes, and a future center/right alignment or an ellipsis/overflow decision would render differently than the old widget would have.",
+    "Low blast radius: one screen in one app, no shared code modified, no consumer of design_system affected."
+  ],
+  "rollback": [
+    "git revert the commit — the change is self-contained in one file.",
+    "After rollback, confirm `flutter analyze` is clean and the People screen still shows the 'People' and 'Groups' headings with 16px gutters."
+  ]
+}